Try:

sub equate2 {
    my ($self, $other, $mapping) = @_;
    my $sm = $self->{Matrix};
    my $om = $other->{Matrix};
    for my $row ( 0 .. $#$mapping ) {
        my $smrow = $sm->[ $row ];
        my $omrow = $om->[ $mapping->[ $row ] ]; 
        for my $col ( 0 .. $#$mapping ) {
            return 0 if $smrow->[ $col ] != $omrow->[ $mapping->[ $col
+ ] ];
        }
    }
    return 1;
}
[download]

I am in your debt!!!!! In my test case this is 40% faster, that's going to save me a couple of days right there.

How big is $mapping? (And can you show us (some of) what it contains? Eg. the mapping sequence.)

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